Bosons are a class of particles existing in nature which include objects of different kinds but sharing a common behaviour. Major examples are helium and rubidium and some quanta carrying forces like photons for electromagnetism. These particles exhibit Bose-Einstein Condensation (BEC): when bosons go through BEC, at extremely low temperatures they suddenly begin to act as a single quantum entity, giving rise to new states of matter with peculiar properties such as superfluidity — the ability to flow without resistance. BEC has been observed experimentally but has not a complete and rigorous mathematical understanding. In particular, our theoretical understanding of the fundamental energy laws governing Bose gases remains incomplete.
A central question is: is it possible to identity universal laws to calculate the energy of bosonic systems?
The project UniBoGas tackles this problem by providing a unified mathematical description of the energy of bosons. It focuses on whether the energy of dilute Bose gases of different kinds, including different species of bosons and interactions with repulsive and attractive forces, can be described universally, that is, independently of the detailed shape of the interaction between the particles. Main core of the project is to show, indeed, how different kinds of bosonic systems have a common pattern and behave energetically as systems of hard spheres colliding (like billiards), and the energy can be found by formulas depending only on the diameter of such spheres.
The project addresses this problem following three research lines:
• It investigates whether universal formulas can be used to calculate the energy for systems of bosons interacting through forces which are not purely repulsive. Most of the bosonic systems considered in experiments and in chemical models are included in this category.
• It shows how it is possible to calculate with universal formulas the energy of mixtures of two boson species, which are of growing experimental interest.
• It deals with the calculation of energy levels beyond the minimal energy configuration, to include excited energy states, which are crucial for linking theoretical predictions to what is measured in the lab.
Obtaining universal formulas for these broad classes of Bose gas systems greatly simplifies the evaluation of their energy, with potential impact not only in Mathematical Physics but also in fields such as Quantum Chemistry and quantum technologies. The results obtained in UniBoGas contribute to the fundamental, theoretical research on BEC, which in turn will help the technological development in quantum optics and quantum computers.
